If tan 2 θ = cot ( θ - 36°), where 2 θ is an acute angle, then the value of θ is:

If tan 2 θ = cot ( θ - 36°), where 2 θ is an acute angle…

If tan 2 $\theta$ = cot ( $\theta$ - 36°), where 2 $\theta$ is an acute angle, then the value of $\theta$ is:

Show answer & explanation

Correct answer: D

Explanation

The correct answer is option 4 i.e. 42°.

tan 2θ = cot(θ - 36°)

⇒ tan 2θ = tan[90° - (θ - 36°)]

⇒ tan 2θ = tan(126° - θ)

⇒ 2θ = 126° - θ

⇒ 3θ = 126°

⇒ θ = 126°/3 = 42°

Therefore, the value of θ is 42°.